Finite Group Databasebeta

← Prev (#14601064) Next (#14601066) →

C11×#23872 #14601065

order2816
nilpotency class3
isoclinismisoclinic class of #23872
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23872

Subgroups

subgroupG/H
center, socleC2×C11#2403
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 4 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,17)(16,20)(18,22)(19,24)(23,27)(25,26);(13,17)(15,24)(18,21)(19,20)(22,25)(26,27);(15,24)(17,19)(21,27)(22,25);(12,14)(13,18)(15,25)(16,23)(17,21)(19,27)(20,26)(22,24)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD11×#23872
maximal subgroup ofD11×#23872
maximal normal subgroup ofD11×#23872

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16860);